This invention relates to method and apparatus for uniformly mixing liquids in an environment wherein the velocity of liquid flow is defined by a Reynolds number less than 1.
The normal means of mixing two or more miscible liquids is to stir (either mechanically with a blade or by using fluid inertial forces) to produce a high rate of fluid flow that, in turn, produces large inertial forces within the liquid to create turbulence, which by its nature, provides a large interfacial surface area between the liquids such that diffusion of the liquids into each other can take place readily to produce a single homogeneous liquid. However, when the velocity of flow of the liquids is very small (creeping flow), i.e., the Reynolds number R=Ud/v&lt;1, wherein U=mean flow velocity, d=the diameter of the flow channel, and v=the kinematic viscosity, such as might be encountered in capillary systems, fluid viscous forces completely dominate the fluid inertial forces produced by high rates of fluid flow owing to the small length scales and low velocities. In this case the inertial forces that produce turbulence and the resultant large interfacial surface areas necessary to promote mixing are absent. Thus, the only mixing that can occur in creeping flow is by diffusion through a limited interfacial area. Since, in general, in those systems in which creeping flow is the dominant mode of liquid flow, the ratio of interfacial surface area to volume is very small, mixing two liquids to produce a single homogeneous liquid can be a slow process requiring the two liquids to be in contact for extended periods of time. For many applications where two or more miscible liquids must be mixed and dispensed rapidly but which must operate in the creeping flow regime, such as generally the case in capillary systems, this is unacceptable. What is needed is a means for rapidly producing a single homogeneous liquid by mixing two or more liquids in a creeping flow regime.
An alternative method to create interface in a liquid in the low Reynolds number limit is to repeatedly: 1) divide the liquid into two or more flow streams, 2) physically rotate the flow streams about the flow axis, and 3) recombine the divided liquid. This can only be achieved by providing for flow out of the plane which requires a multilevel fluidic structure which, can be disadvantageous.
It has long been known that liquids, and particularly electrolytes, can be caused to flow by virtue of electroosmotic flow. Electroosmotic flow is attributable to the formation of an electric double layer at the interface between a solid that is a dielectric material and a liquid capable of charge separation, generally an electrolyte. As a consequence of the formation of the electric double layer, a electrically charged diffuse layer is formed in the liquid extending from the solid-liquid interface into the bulk of the liquid. Under the influence of a tangential electric field, produced by electrodes having an electric potential applied thereto, and, in contact with the liquid, the diffuse layer is caused to move. The liquid will now flow as a consequence of the force (electroosmotic force) developed between the moving liquid and the wall of the dielectric material. Furthermore, the liquid will flow at a constant rate depending upon the equilibrium established between frictional forces. Thus, in the low Reynolds number limit, an increase in the liquid interface can only be achieved through repeated laminar folding of the liquid, such as can be achieved by electroosmotic flow.
By taking advantage of electroosmotic flow it is possible to rapidly mix two or more miscible liquids together to form a homogeneous liquid without mechanical stirring.